# Is modus ponens an invalid rule in Aristotelian logic?

I am a beginner in Aristotelian logic and I was wondering that Aristotle does not pay attention to conditional propositions in his logic and only has focused on categorical syllogisms. Does this means that modus ponens is not a valid rule for Aristotle? It is a clear inference rule and Why didn't he include it in his logical system?

• "Why didn't he include it in his logical system?" Because A's logic was not a system of propositional logic. For a modern point of view, see John Corcoran, A Mathematical Model of Aristotle’s Syllogistic (1973) as well as John Corcoran, Aristotle's natural deduction system (1974). Dec 12, 2022 at 14:17
• Having said that, MP is not invalid: it is not used. Dec 12, 2022 at 14:21
• And see Susanne Bobzien, The Development of Modus Ponens in Antiquity (2002) Dec 12, 2022 at 14:31
• I see that, but it is clear inference rule and why Aristotle missed it? If he wanted to built the most general laws of thought. Dec 12, 2022 at 14:36
• "he wanted to built the most general laws of thought"... but restricted to a certain "logical structure" of statements: "P is affirmed of all (some) of S". Dec 12, 2022 at 14:40

Aristotle's logic, also known as syllogistic logic, is a system of logic that is based on the principles of the syllogism, which is a type of argument consisting of three propositions. In syllogistic logic, only categorical propositions are considered, and conditional propositions, such as modus ponens, are not included in the system.

Modus ponens is a valid rule of inference, and it allows us to draw a conclusion from two premises, one of which is a conditional proposition. For example, if we know that "if A is true, then B is true" and we also know that "A is true," then we can infer that "B is true" using modus ponens.

However, Aristotle's logic does not include conditional propositions, and therefore, modus ponens is not a part of his logical system. Aristotle's logic focuses on categorical propositions, which are statements that assert or deny a relationship between two categories, such as "all A are B" or "no A are B." These propositions are the building blocks of syllogistic logic, and they are used to construct syllogisms and deduce conclusions from them.

It is not clear why Aristotle did not include conditional propositions in his logic, but one possible reason is that he was primarily interested in the study of syllogisms and their role in argumentation and persuasion. Conditional propositions were not part of this study, and therefore, they were not included in Aristotle's logical system.

However, this does not mean that conditional propositions are not important or useful in logic. In fact, many other logicians and philosophers have studied and developed rules for dealing with conditional propositions, and modus ponens and other rules of inference involving conditional propositions are commonly used in modern logic and reasoning.

• Thank you so much, I know that modus ponens is a very important inference rule in modern logic, but it was obscure that Aristotle has not considered them seriously. I feel that he did not pay attention to conditionals based on some logical reasons. It is strange if he has not referred to conditionals in organon. Dec 12, 2022 at 21:07
• Aristotle didn't really concern himself with what we would now call propositional logic - the logic of and/or/not/if. That came about a century later when the stoic philosophers such as Chrysippus, Diodorus and Philo developed it. I suppose one cannot expect Aristotle to do everything. Dec 14, 2022 at 11:40

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

It seems to me that MP is buried in the "therefore."

In the notation of modern predicate logic, with line 4 being an application MP (Detachment):

• But "Socrates is mortal" is NOT a categorical proposition according to A's original texts. Dec 15, 2022 at 10:25
• @MauroALLEGRANZA, How does Aristotle analyze these sentences? Dec 16, 2022 at 13:35

All X are Y [universal affirmative in Aristotle's categorical logic] is logically equivalent to If X then Y [conditional in predicate logic].

So All men are mortal = If a man then mortal.

Consider now the categorical syllogism below

1. All men are mortal
2. Socrates is a man
Ergo,
3. Socrates is mortal

In predicate logic it is

1. If x is a man then x is mortal
2. Socrates is a man (x = Socrates)
3. Socrates is mortal (x i.e. Socrates is mortal) [1, 2 modus ponens]
• But "Socrates is mortal" is NOT a categorical proposition according to A's original texts. Dec 15, 2022 at 10:24
• All men are mortal (categorical logic) = If (x is a man) then (x is mortal). Dec 15, 2022 at 14:53
• Dec 15, 2022 at 14:56
• Will do. Danke. Dec 15, 2022 at 15:24